Is there any relation between L and h in the beam to classify it as slender, intermediate, or short? Neglecting the use of relations obtained in norms.
Quantification of beams like has less meaning, it also related with material and cross-sectional shape. Whether an E-B model is applicable or not is not directly related with such simplistic slenderness characterization either. My opinions related with this issue can be found at https://cdmhub.org/groups/yugroup/blog/2016/12/structures-models--assumptions.
Yes. Nearly. The relation is between the shear span typically called a of the beam and the effective height of the beam typically called d.
The effective height is the distance from the top of the concrete in the compression zone to the centre of gravity of the tensile reinforcement.
The shear span was described by Kani as the distance between the support and the load in a simple four point beam. More generally it has been described as the distance from the zero point of the bending moment curve to the applied load.
When a/d is less than one, we call it a deep beam.
When a/d is between one and 2.5, we call it a short beam.
When a/d is larger than 2.5, we call it a slender beam.
Hello Asger,
I'm grateful for your response.
My question arises from the problem of finding in many books the quotation regarding the slender beam, but in a few I have found a relation (L / h) that can express this limit (Slender, intermediate, short).
I have already found some relationships when looking at standards for concrete, wood and steel beams. However, my goal would be to find a relation to characterize the beam as slender independent of the material, which in the case of the findings found in standards present considerations on the material used in the beam.
Hi prof. Wenbin,
My motivation arises from the problem of not finding in books of Strenght of Materials, Solid Mechanics and Mechanics of Materials a relation to classify the beam as slender, in some books I have found a relation.
In Mechanics of Materials by Barry J. Goodno and James M. Gere, I found L / h < 10 is stocky beam.
In Buckling of Bars, Plates, and Shells by Robert Millard Jones, I found L / h > 10 and L / h> 5 to classify as a slender beam.
In An Introduction to the Mechanics of Solids by Stephen H. Crandall, I found L / h > 5 to classify as a slender beam.
In most books the slender beam classification is used in a context of Euler-Bernoulli Beam Theory, strain energy analysis. However, it seems to me that the quantification of the beam's slenderness is not yet common and well defined for all.
Quantification of beams like has less meaning, it also related with material and cross-sectional shape. Whether an E-B model is applicable or not is not directly related with such simplistic slenderness characterization either. My opinions related with this issue can be found at https://cdmhub.org/groups/yugroup/blog/2016/12/structures-models--assumptions.
Hi prof. Marek
Thanks for the answer. I found something the same in other books, as I have posted here in the answers. I get the following question:
If L/h < 5 for deep short beam, knowing this we can classify a slender beam using the ratio L/h> 5?
The real question of some importance is what is an accuracy of the results obtained due to theory of beams as compared with theory of elasticity. This accuracy may depend on a number of parameters, not only L/h. Ugural suggested in his Mechanics of Materials that results are good for metal beams of compact section with L/h>10, for beams with relatively thin webs and L/h>15, and for rectangular timber beams as L/h>24.
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